Abstract: Orientation-dependent growth phenomena have been observed for liquid-phase epitaxial In1-xGaxAs and other ternary and quaternary III-V semiconductors. The data cannot be explained by existing regular solution phase equilibria models. In this study we have used the quasi-regular solution formulation to derive a model which also considers equilibrium between the growing surface and the bulk solid under it. Orientation-dependent parameters characterizing the growing surface in the (100) and (111) directions have been included. The model is demonstrated for growth of In1-xGaxAs at 650 and 621[deg]C. Excellent agreement is obtained with data for growth of the ternary on (lll)B InP substrates, whereas some adjustment of the parameters are necessary to obtain similar agreement in case of growth on (100)-oriented substrates.